Experts recognize artistic style by invoking knowledge of plastic elements and their juxtaposition. Algorithmic methods now make it possible for this knowledge to be expressed to a computer. Compared to the alternative of describing style in natural language, the computer methods offer the advantage that they can be tested for validity. The tests are accomplished by using the computer to generate new compositions in the style described. The authors demonstrate these methods with algorithmic descriptions of the styles of Richard Diebenkorn and Joan Miró and the generation of new compositions in their styles. A shape grammar algorithm for Diebenkorn is presented which accounts for the linear facture of his <i>Ocean Park</i> series. The problem of shape in Miró's work is tackled, and progress is reported on synthesizing composition in the style of his <i>Constellation</i> series. Further uses of algorithmic description of painting styles include mechanical storage, search and retrieval in art archives, attribution studies and diachronic studies of stylistic change.